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%I #7 Mar 31 2021 01:28:02
%S 0,1,1,4,8,4,9,25,25,9,16,52,80,52,16,25,89,169,169,89,25,36,136,292,
%T 360,292,136,36,49,193,449,625,625,449,193,49,64,260,640,964,1088,964,
%U 640,260,64,81,337,865,1377,1681,1681,1377,865,337,81,100,424,1124,1864,2404,2600,2404,1864,1124,424,100
%N Triangle T(n, k) = n^2 + (2*k*(n-k))^2, read by rows.
%H G. C. Greubel, <a href="/A141402/b141402.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = n^2 + (2*k*(n-k))^2.
%F Sum_{k=0..n} T(n, k) = n*(2*n^4 + 15*n^2 + 15*n -2)/15. - _G. C. Greubel_, Mar 30 2021
%e Triangle begins as:
%e 0;
%e 1, 1;
%e 4, 8, 4;
%e 9, 25, 25, 9;
%e 16, 52, 80, 52, 16;
%e 25, 89, 169, 169, 89, 25;
%e 36, 136, 292, 360, 292, 136, 36;
%e 49, 193, 449, 625, 625, 449, 193, 49;
%e 64, 260, 640, 964, 1088, 964, 640, 260, 64;
%e 81, 337, 865, 1377, 1681, 1681, 1377, 865, 337, 81;
%e 100, 424, 1124, 1864, 2404, 2600, 2404, 1864, 1124, 424, 100;
%p A141402:= (n,k)-> n^2 + (2*k*(n-k))^2;
%p seq(seq(A141402(n,k), k=0..n), n=0..12); # _G. C. Greubel_, Mar 30 2021
%t T[n_, k_]:= n^2 + (2*k*(n-k))^2;
%t Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
%o (Magma) [n^2 + (2*k*(n-k))^2: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 30 2021
%o (Sage) flatten([[n^2 + (2*k*(n-k))^2 for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 30 2021
%K nonn,easy,tabl
%O 0,4
%A _Roger L. Bagula_, Aug 03 2008
%E Edited by _G. C. Greubel_, Mar 30 2021
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